Given positive integer $N$ and parameters $T>0$, $a$, $b$, what is
$\int_{t_1=0}^T \cdots \int_{t_N=0}^T e^{a(t_1+\cdots+t_N)+b(t_1t_2+\cdots+t_{i1}t_i+t_Nt_1)} dt_1 \cdots dt_N$ ?
Any thought will be very much appreciated!
Given positive integer $N$ and parameters $T>0$, $a$, $b$, what is $\int_{t_1=0}^T \cdots \int_{t_N=0}^T e^{a(t_1+\cdots+t_N)+b(t_1t_2+\cdots+t_{i1}t_i+t_Nt_1)} dt_1 \cdots dt_N$ ? Any thought will be very much appreciated! 

